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For a circular coil of radius R and N turns carrying current I, themagnitude of the magnetic field at a point on its axis at a distance xfrom its centre is given by,( )202 2 3/2 2IR NBx Rμ=+(a) Show that this reduces to the familiar result for field at thecentre of the coil.(b) Consider two parallel co-axial circular coils of equal radius R,and number of turns N, carrying equal currents in the samedirection, and separated by a distance R. Show that the field onthe axis around the mid-point between the coils is uniform overa distance that is small as compared to R, and is given by,0 0.72NIBRμ= , approximately.[Such an arrangement to produce a nearly uniform magneticfield over a small region is known as Helmholtz coils.] |
| Answer» For a circular coil of radius R and N turns carrying current I, themagnitude of the magnetic field at a point on its axis at a distance xfrom its centre is given by,( )202 2 3/2 2IR NBx Rμ=+(a) Show that this reduces to the familiar result for field at thecentre of the coil.(b) Consider two parallel co-axial circular coils of equal radius R,and number of turns N, carrying equal currents in the samedirection, and separated by a distance R. Show that the field onthe axis around the mid-point between the coils is uniform overa distance that is small as compared to R, and is given by,0 0.72NIBRμ= , approximately.[Such an arrangement to produce a nearly uniform magneticfield over a small region is known as Helmholtz coils.] | |